Restriction on the strong coupling constant in the IR region from the 1D-1P splitting in bottomonium

Abstract

The bb spectrum is calculated with the use of a relativistic Hamiltonian where the gluon-exchange potential between a quark and an antiquark is taken as in background perturbation theory. We observed that the splittings ∆ 1 = Υ(1D) − χ b (1P) and other splittings between low-lying states are very sensitive to the QCD constant Λ V (n f ) which occurs in the Vector scheme, and good agreement with the experimental data is obtained for Λ V (2-loop, n f = 5) = 325 ± 10 MeV which corresponds to the conventional Λ MS (2−loop, n f = 5) = 238 ± 7 MeV, α s (2−loop, M Z ) = 0.1189 ± 0.0005, and to a large freezing value of the background coupling: α crit (2-loop, q 2 = 0) = α crit (2-loop, r → ∞) = 0.58 ± 0.02. If the asymptotic freedom behavior of the coupling is neglected and an effective freezing coupling α static = const is introduced, as in the Cornell potential, then precise agreement with ∆ 1 (exp) and ∆ 2 (exp) can be reached for the rather large Coulomb constant α static = 0.43 ± 0.02. We predict a value for the mass M (2D) = 10451 ± 2 MeV.

Strange baryon spectroscopy in the relativistic quark model

“…with the background mass M B = 2.24 √ A = 0.95 GeV [18] and Λ = 413 MeV [19]. All parameters of the model were fixed previously from calculations of meson and baryon properties [17].…”

NJL Interaction Derived From QCD

“…This assumption is very close to conception of frozen strong coupling at low momenta [13]. The consideration of average low-momenta value of α s [13,14,15,16] leads to definition of a possible range of values of α s from 0.45 up to 0.75. So in what follows we use constant α s which is assumed to fit this interval of possible values.…”

Spectroscopic properties of the B meson

“…where M = 2m Q mq/ m Q + mq , M B = 0.95 GeV [16,17], and Λ = 0.413 GeV [18]. We have used the gaussian wave function in the present study.…”

“…The value of the QCD coupling constant α s (M 2 ) is determined through the simplest model with freezing [16,17], namely…”